AntiFragility: Tough times don't last - tough people do!

13 Pages·2013·0.15 MB·English

September 2013
AntiFragility:
Tough times don’t last -
tough people do!
Presented by Claus Madsen:
CEO FinE Analytics, Partner InRisk,
Associate Professor DTU - FE,
Chairman of the Risk Management Network,
Regional Director Denmark PRMIA
E-mail: [email protected],
[email protected]
Fragile, Robust and Anti-Fragile?
Fragile: The cumulative effect of small shocks is smaller than
the single effect of an equivalent single large shock
That is: Fragility is related to how a system suffers from the
variability of its environment beyond a certain preset
threshold (when threshold is K, it is called K-fragility)

Robust: The resilient resists shocks and stays the same

Antifragile: Refers to when the system benefits from variability.
The antifragile loves randomness and uncertainty
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Tail-Events......I
 A coffee cup on a table suffers more from large shocks than
from the cumulative effect of some shocks. Conditional on being
unbroken, it has to suffer more from “tail” events than regular
shocks around the center of the distribution, the “at the money”
category
This is the case of elements of nature that have survived:
conditional on being in existence, in this case the class of
events around the mean should matter considerably less than
tail events

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Tail-Events......II
 Systems which has exposure to tail events suffers from
uncertainty; typically, when systems – a building, a bridge, a
nuclear plant, or a bank balance sheet– are made robust to a
certain level of variability and stress but may fail or collapse if
this level is exceeded
 In this case these systems are particularly fragile to
uncertainty about the distribution of the stressor, hence to
model error, as this uncertainty increases the probability of
dipping below the robustness level, bringing a higher
probability of collapse

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Tail-Events......III
Opposite fragile we have that the natural selection of an
evolutionary process is particularly antifragile, indeed, a more
volatile environment increases the survival rate of robust species
and eliminates those whose superiority over other species is
highly dependent on environmental parameters
…………….
When it comes to random events “robust” is certainly not good
enough.
We need a mechanism by which a system regenerates itself
continuously by using, rather than suffering from, random
events, unpredictable shocks, stressors, and volatility.
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Intrinsic and Inherited Fragility
 The earlier definition of fragility relies on the nonlinearity of
exposure as nonlinearity in a source of stress is necessarily associated
with fragility
Clearly, a coffee cup, or a bridge don’t have subjective utility
functions, etc. Yet they are concave in their reaction to harm: simply,
taking z as a stress level and Π(z) as the harm function, it suffices to see
that, with
n > 1, Π(nz) < n Π( z) for all 0 < nz < Z*
where Z* is the level (not necessarily specified) at which the item is
broken. Such inequality leads to Π(z) having a negative second derivative
at the initial value z
Hint: Fragility that comes from the effect of the underlying is called
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inherited fragility
Detection Heuristic
 The main idea is that a wrong ruler will not measure the height
of a child; but it can certainly tell us if he is growing
Since risks in the tails map to nonlinearities (concavity of
exposure), second order effects reveal fragility, particularly in the
tails where they map to large tail exposures, as revealed through
perturbation analysis.
More generally every nonlinear function will produce some kind
of positive or negative exposures to volatility for some parts of
the distribution

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Fragility and Model Error – I
 The definition of fragility extends to model error, as some
models produce negative sensitivity to uncertainty, in addition to
effects and biases under variability.
So, beyond physical fragility, the same approach measures
model fragility, based on the difference between a point estimate
and stochastic value (i.e., full distribution). Increasing the
variability (say, variance) of the estimated value (but not the
mean), may lead to one-sided effect on the model

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Fragility and Model Error - II
 For instance, the misuse of thin-tailed distributions (say
Gaussian) appears immediately through perturbation of the
standard deviation:
 No longer used as point estimate, but as a distribution with
its own variance.
For instance, it can be shown how fat-tailed (e.g. power-law
tailed) probability distributions can be expressed by simple
nested perturbation and mixing of Gaussian ones:
Such a representation pinpoints the fragility of a wrong
probability model and its consequences in terms of
underestimation of risks, stress tests and similar matters.
Reference: Taleb and Douady, ” Mathematical Definition, Mapping, and
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Detection of (Anti)Fragility”, August 2012
Definition, Mapping, and Detection of (Anti)Fragility

Reference: Taleb and Douady, ” Mathematical
Definition, Mapping, and Detection of (Anti)Fragility”,
August 2012
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